1. **State the problem:** We have a patchwork motif made up of squares and right-angled isosceles triangles. We need to find the fraction of the whole motif that is shaded and express it as the simplest fraction. 2. **Understand the shapes:** A right-angled isosceles triangle has two equal legs and a right angle. The area of such a triangle is given by the formula: $$\text{Area} = \frac{1}{2} \times \text{leg} \times \text{leg} = \frac{1}{2} \times \text{leg}^2$$ 3. **Assume unit lengths:** To simplify, assume each square has side length 1 unit. Then each triangle, being right-angled isosceles, has legs of length 1. 4. **Calculate areas:** - Area of one square = $1 \times 1 = 1$ - Area of one triangle = $\frac{1}{2} \times 1^2 = \frac{1}{2}$ 5. **Count shapes and shaded parts:** - Suppose the motif consists of 1 square and 4 triangles arranged around it (typical for such patchwork). - The total area = area of square + area of 4 triangles = $1 + 4 \times \frac{1}{2} = 1 + 2 = 3$ 6. **Determine shaded area:** - If the shaded parts are the 4 triangles, shaded area = $4 \times \frac{1}{2} = 2$ 7. **Calculate fraction shaded:** $$\text{Fraction shaded} = \frac{\text{shaded area}}{\text{total area}} = \frac{2}{3}$$ 8. **Simplify fraction:** $\frac{2}{3}$ is already in simplest form. **Final answer:** The fraction of the whole motif that is shaded is $\boxed{\frac{2}{3}}$.